]> 2026-05-15T03:12:39-03:00 Control Design for Constrained LTI and LPV Systems via Polyhedral Set Invariance 0 pt-br engenharia de automacao e sistemas invariancia realimentacao sistema lti sistema lpv controle Castelan Neto, Eugênio de Bona Camponogara, Eduardo Universidade Federal de Santa Catarina. Programa de Pós-Graduação em Engenharia de Automação e Sistemas Ernesto, Jackson Gonçalves 2024 2460310.5 131 p. Inglês Jackson Gonçalves Ernesto ; orientador, Eugênio de Bona Castelan Neto ; coorientador, Eduardo Camponogara Control Design for Constrained LTI and LPV Systems via Polyhedral Set Invariance B000127 2024-10-09T19:00:01Z 2460593.2916782 Control Design for Constrained LTI and LPV Systems via Polyhedral Set Invariance 2024-10-09T19:00:34Z 2460593.2920602 Control Design for Constrained LTI and LPV Systems via Polyhedral Set Invariance 0 0 plainlist 1 [[:B000127#000]] Control Design for Constrained LTI and LPV Systems via Polyhedral Set Invariance# QUERY71d60bc23bfa6c72633923fc85b6a8f6 0 0 plainlist 1 [[:B000127#245]] Control Design for Constrained LTI and LPV Systems via Polyhedral Set Invariance# QUERY3d59e65bc89eb919fcb03881ea569d10 0 0 plainlist 1 [[:B000127#008]] Control Design for Constrained LTI and LPV Systems via Polyhedral Set Invariance# QUERYb8023fd50629859a41d0f3ea320465ff 0 0 plainlist 1 [[:B000127#020]] Control Design for Constrained LTI and LPV Systems via Polyhedral Set 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[[:B000127#130]]</q> Control Design for Constrained LTI and LPV Systems via Polyhedral Set Invariance# QUERYc314e4a55ec59f37db647d85652ada31 0 00325 001000800000003000900008005001700017008004100034040003800075090002700113100003200140245021900172260001000391300001800401500004400419502017700463504002500640520346400665520282004129650004106949650001706990650002007007650001607027650001607043650001307059700004907072700004007121710011407161856006907275 00000nam a2200000 a 4500 07670 000 0 241009s2024    scba   g m    000 0 eng d 008 0 ##$a BR-FlWIK $b por $c BR-FlWIK $d BR-FlUSC 040 0 ##$a CETD $b UFSC $c PEAS $d 0456 090 0 1#$a Ernesto, Jackson Gonçalves 100 0 10$a Control Design for Constrained LTI and LPV Systems via Polyhedral Set Invariance $h [recurso eletrônico] / $c Jackson Gonçalves Ernesto ; orientador, Eugênio de Bona Castelan Neto ; coorientador, Eduardo Camponogara 245 0 ##$c 2024. 260 0 ##$a 131 p. : $b il. 300 0 ##$a Disponível somente em versão on-line. 500 0 ##$a Tese (doutorado) – Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia de Automação e Sistemas Florianópolis, 2024. 502 0 ##$a Inclui referências. 504 0 ##$a Neste trabalho, os conceitos de invariância e contratividade aplicados a conjuntos poliedrais são utilizados para projetar leis de controle por realimentação de saídas e determinar regiões de estabilidade local para sistemas discretos lineares invariantes no tempo e sistemas lineares a parâmetros variantes no tempo. Os sistemas controlados podem estar sujeitos a restrições de estado, controle e variação do controle,e a perturbações persistentes limitadas. Primeiramente, é utilizado a propriedade de Invariância Positiva Robusta (RPI), também chamada de ∆-Invariância, de conjuntos poliedrais para projetar uma lei de controle por realimentação estática de saídas para sistemas lineares e invariantes no tempo sujeitos a perturbações persistentes, garantindo que as restrições de estado e controle sejam satisfeitas. Condições algébricas são deduzidas para garantir que qualquer trajetória que se inicie no poliedro ∆-invariante permanece nele e convirja em tempo finito para outro conjunto poliedral ao redor da origem, onde a trajetória permanecerá ultimamente limitada. Assim, a solução por realimentação estática de saídas proposta para o sistema de controle restrito também requer a determinação dos conjuntos ∆-invariante e ultimamente limitado.A seguir, são utilizados os conceitos conjuntos de conjuntos Robustos Controlados Invariantes (RCI) e Robustos Controlados a um Passo (ROSC) para obter um controlador chaveador por realimentação de saídas que guia as trajetórias do sistema restrito à origem em um certo número de passos amostrais. Um conjunto de ganhos estáticos de realimentação de saídas é computado de maneira offline, que mais tarde compõe o controlador chaveado. Na sequência, baseado nas condições algébricas que descrevem de forma equivalente à invariância positiva de conjunto poliedrais para sistemas discretos Lineares a Parâmetros Variantes (LPV), é proposta a abordagem para o projeto de controladores incrementais por realimentação de saídas que garantam a estabilidade assintótica local em malha fechada, com o cumprimento das restrições de estado e controle. O controlador incremental por realimentação de saídas proposto realimenta as saídas medidas e as entradas de controle. O projeto de controle sob restrições permite, em particular, lidar com restrições na variação do controle por meio de uma lei de controle a parâmetros variantes. Finalmente, o projeto da lei de controle incremental LPV é estendida para lidar com perturbações limitadas persistentes. Neste caso, visando buscar soluções menos conservadores, propõe-se utilizar um ganho adicional à lei de controle. As condições algébricas de projeto propostas são traduzidas em problemas bilineares de otimização bilineares. Cada Problema Bilinear (BP) considera uma função objetivo que otimiza o tamanho do poliedro em um conjunto dado de direções, ponderando o tamanho do poliedro associado (quando necessário), e suas restrições são formadas pelas condições de invariância positiva robusta e inclusões de conjuntos usadas para garantir o cumprimento das restrições. Um solver não-linear eficiente (KNITRO) e linguagem de programação AMPL são utilizados para lidar com as bilinearidades presentes nos problemas de otimização. Exemplos numéricos apresentados ao longo do documento demonstram o potencial e efetividade das técnicas propostas. 8#$a Abstract: In this work, set invariance concepts applied to polyhedral sets are used to design stabilizing Output Feedback (OF) control laws for linear time-invariant (LTI) and linear parameter varying (LPV) discrete-time systems. The constrained controlled system may be subject to state, control amplitude, and control-rate constraints, and persistent disturbances. Firstly, we use the Robust Positive Invariance (RPI) property (also called ∆-Invariance) of polyhedral sets to design a stabilizing static Output Feedback (OF) control law for linear discrete-time systems subject to persistent disturbances, assuring the states and control constraints fulfillment. We deduce algebraic conditions to guarantee that any trajectory emanating from the∆-Invariant polyhedron remains in it and converges in finite time to another polyhedral set around the origin, where the trajectory remains ultimately bounded. Thus, the proposed staticOF solution for the constrained control problem also requires determining the∆-invariant and the ultimately bounded polyhedra. Next, we use the joint concepts of Robust Control Invariant (RCI) set and Robust OneStep Controllable sets (ROSC) to obtain a switching output regulator that steers the constrained system’s trajectory to the origin in a certain number of sample periods. A set of static output feedback control gains is computed offline, which later compose the online switching regulator. Then, based on the necessary and sufficient algebraic conditions that describe the polyhedral positive-invariance for LPV systems, we propose an incremental controller design, guaranteeing the regional closed-loop stability and that the control and state constraints are all respected. The proposed incremental output feedback controller feeds back both the measured outputs and control inputs. The constrained control design allows, inparticular, dealing with the control-rate variation bounds through a parameter-varying control law. Additionally, an alternative implementation is proposed, where the state and control constraints build part of the positive invariant set. Moreover, we extend the proposed LPV incremental control law design to deal with bounded persistent disturbances. The proposed algebraic design conditions are translated into bilinear optimization problems. Each Bilinear Problem (BP) considers an objective function that optimizes the polyhedron size in given directions, weighting the size of associated polyhedral sets (when necessary), whose constraints are formed by the robust positive invariance conditions and set inclusions. An efficient non-linear optimization solver (KNITRO) is employed to tackle the present bilinearities through the AMPL language. Furthermore, numerical examples showcase the proposals’ effectiveness and potential. 520 0 04$a Engenharia de automação e sistemas 04$a Invariância 04$a Realimentação 04$a Sistema LTI 04$a Sistema LPV 04$a Controle 650 0 1#$a Castelan Neto, Eugênio de Bona, $e orientador 1#$a Camponogara, Eduardo, $e coorientador 700 0 2#$a Universidade Federal de Santa Catarina. $b Programa de Pós-Graduação em Engenharia de Automação e Sistemas 710 0 40$z Versão integral em pdf $u https://bu.ufsc.br/teses/PEAS0456-T.pdf 856 0 B000127 001 0 BR-FlWIK 003 0 20241009160034.0 005